\documentclass[12pt,a4paper]{book}
\input{intro}

\author{Leonardo}
\title{DESlab functions}
\begin{document}

\chapter{Exhaustive analysis of diagnosability }



\begin{table}
\begin{tabular}{llllccc}
\toprule
$(||X||,||\Sigma||)$ & Total & Valid & Diag. &  $\max(||D||)$  & $\max(||V||)$\\
\midrule
\midrule
\\
$(2,2)$ & 45 & 9 & 3 &  4 & 6 \\ 
$(2,3)$ & 513 & 117 & 25 &  7 & 6 \\
$(2,4)$ & 5265 & 1215 & 159 & 7 & 6 \\ 
$(2,5)$ & 51273 & 11745 & 913 &  7 & 6  \\ 
$(3,2)$ & 816 & 161 & 47 &  9 & 12  \\ 
$(3,3)$ & 81856 & 18709 & 1988 &  20 & 12  \\
$(3,4)$ & 6516480 & 1528511 & 65417 &  21 & 12  \\
$(3,5)$ & 467590144 & 10830975 & 612090 &  21 & 12  \\
$(4,2)$ & 20225 & 3384 & 938 &  16 & 20  \\
$(4,3)$ & 23846125 & 4584163 & 243598 & 53 & 20  \\ 
$(5,2)$ & 632700 & 90533 & 24092 & 25 & 30  \\ 
\\ 
\midrule
\bottomrule
\end{tabular}

\caption{Exhaustive test of the complexities of diagnoser and verifier for some families $(||X||,||\Sigma||)$ of automata with ``moderate'' size.}
\label{tab:exhtest}
\end{table}


\begin{table}
\begin{tabular}{cccccc}
\toprule
$(||X||,||\Sigma||)$ & $\overline{||D||}$ & $\overline{||V||}$ & $P(V)$ & $P(D)$ & $P(D|V)$ \\
\midrule
\midrule
\\
$(2,2)$ &  2.44  & 3.44 & 0.2000 & 0.0666 & 0.3333 \\ 
$(2,3)$ &  3.38  & 3.96 & 0.2280 & 0.0487 & 0.2136 \\
$(2,4)$ &  4.18  & 4.39 & 0.2307 & 0.0301 & 0.1308 \\ 
$(2,5)$ &  4.81  & 4.74 & 0.2290 & 0.0178 & 0.0777 \\ 
$(3,2)$ &  3.12  & 5.85 & 0.1973 & 0.0575 & 0.2919 \\ 
$(3,3)$ &  5.87  & 7.58 & 0.2285 & 0.0242 & 0.1062 \\
$(3,4)$ &  8.29  & 8.82 & 0.2345 & 0.0100 & 0.0427 \\
$(3,5)$ &  7.72  & 7.36 & 0.2316 & 0.0013 & 0.0565 \\
$(4,2)$ &  3.58  & 8.81 & 0.1673 & 0.0463 & 0.2771 \\
$(4,3)$ & 8.72  & 12.80 & 0.1922 & 0.0102 & 0.0531 \\ 
$(5,2)$ & 3.97  & 12.17 & 0.1430 & 0.0380 & 0.2661 \\ 
\\ 
\midrule
\bottomrule
\end{tabular}

\caption{Exhaustive test of the complexities of diagnoser and verifier for some families $(||X||,||\Sigma||)$ of automata with ``moderate'' size.}
\label{tab:exhtest}
\end{table}

\newpage



%%% We are going to put the figures
\section{Frequency distribution}

\begin{figure}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Figure-freq-3n-3k}  
\label{freq-3n-3k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Figure-freq-3n-4k}  
\label{freq-3n-4k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Figure-freq-3n-5k}  
\label{freq-3n-5k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Figure-freq-4n-2k}  
\label{freq-4n-2k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Figure-freq-4n-3k}  
\label{freq-4n-3k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Figure-freq-5n-2k}  

}


\caption{Frequency plots of the diagnoser's complexity for automata in Table \ref{tab:exhtest}. }
\label{fig: frequency_plots}
\end{figure}


%%% figure for fitting


\begin{figure}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-FitDist-3n-3k}  
\label{FitDist-3n-2k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-FitDist-3n-4k}  
\label{FitDist-3n-3k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-FitDist-3n-5k}  
\label{FitDist-3n-4k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-FitDist-4n-2k}  
\label{FitDist-4n-2k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-FitDist-4n-3k}  
\label{FitDist-3n-4k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-FitDist-5n-2k}  
\label{FitDist-5n-2k}
}
\caption{Fit of the negative binomial model for the automata in Table \ref{tab:exhtest} }
\label{fig: frequency_plots}
\end{figure}
%
\begin{figure}
\subfloat[][]{%
\includegraphics[width=10cm]{figures/Fig-Dist-X}  
\label{FitCompX}
}\\
\subfloat[][]{%
\includegraphics[width=10cm]{figures/Fig-Dist-S}  
\label{FitCompS}
}\
\caption{Fit of the negative binomial model for the automata in Table \ref{tab:exhtest} }
\label{fig: frequency_plots}
\end{figure}


%%% figure for diagnosability dependence

%%% We are going to put the figures

\begin{figure}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-diagnosiscomp-3n-3k}  
\label{diagnosiscomp-3n-3k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-diagnosiscomp-3n-4k}  
\label{family-3n-3k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-diagnosiscomp-3n-5k}  
\label{family-3n-4k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-diagnosiscomp-4n-2k}  
\label{family-4n-2k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-diagnosiscomp-4n-3k}  
\label{family-3n-4k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-diagnosiscomp-5n-2k}  
\label{family-5n-2k}
}
\caption{Fit of the negative binomial model for the automata in Table \ref{tab:exhtest} }
\label{fig: frequency_plots}
\end{figure}



%%% entropy analysis

\begin{figure}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-entropy-3n-3k}  
\label{entropy-3n-2k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-entropy-3n-4k}  
\label{entropy-3n-3k}
}\\
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-entropy-4n-2k}  
\label{entropy-4n-2k}
}
\subfloat[][]{%
\includegraphics[width=7.5cm]{figures/Fig-entropy-5n-2k}  
\label{entropy-3n-2k}
}
\caption{Fit of the negative binomial model for the automata in Table \ref{tab:exhtest} }
\label{fig: frequency_plots}
\end{figure}




\chapter{Uniform random sampling analysis of diagnosability}
\end{document}